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A Markov Model of Football: Using Stochastic Processes to Model a Football Drive

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  • Goldner Keith

    (Northwestern University)

Abstract

A team is backed into a 4th-and-26 from their own 25, down 3 points. What are the odds that drive ends in a field goal? In the 2003 playoffs, Donovan McNabb and the Eagles scoffed at such a probability as they converted and ultimately kicked a field goal to send the game into overtime. This study creates a mathematical model of a football drive that can calculate such probabilities, labeling down, distance, and yard line into states in an absorbing Markov chain. The Markov model provides a basic framework for evaluating play in football. With all the details of the model—absorption probabilities, expected time until absorption, expected points—we gain a much greater situational understanding for in-game analysis.

Suggested Citation

  • Goldner Keith, 2012. "A Markov Model of Football: Using Stochastic Processes to Model a Football Drive," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(1), pages 1-18, March.
    • Handle: RePEc:bpj:jqsprt:v:8:y:2012:i:1:n:9
    DOI: 10.1515/1559-0410.1400
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    References listed on IDEAS

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    1. Newton Paul K & Aslam Kamran, 2009. "Monte Carlo Tennis: A Stochastic Markov Chain Model," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(3), pages 1-44, July.
    2. Alamar Benjamin C, 2010. "Measuring Risk in NFL Playcalling," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(2), pages 1-9, April.
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    Cited by:

    1. Heiner Matthew & Fellingham Gilbert W. & Thomas Camille, 2014. "Skill importance in women’s soccer," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(2), pages 287-302, June.
    2. Jarvandi Ali & Sarkani Shahram & Mazzuchi Thomas, 2013. "Modeling team compatibility factors using a semi-Markov decision process: a data-driven approach to player selection in soccer," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 9(4), pages 347-366, December.
    3. Yurko Ronald & Ventura Samuel & Horowitz Maksim, 2019. "nflWAR: a reproducible method for offensive player evaluation in football," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(3), pages 163-183, September.
    4. Heiny Erik L. & Heiny Robert Lowell, 2014. "Stochastic model of the 2012 PGA Tour season," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(4), pages 367-379, December.
    5. Yurko Ronald & Ventura Samuel & Horowitz Maksim, 2019. "nflWAR: a reproducible method for offensive player evaluation in football," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(3), pages 163-183, September.
    6. Timothy C. Y. Chan & Craig Fernandes & Martin L. Puterman, 2021. "Points Gained in Football: Using Markov Process-Based Value Functions to Assess Team Performance," Operations Research, INFORMS, vol. 69(3), pages 877-894, May.

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